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arXiv · 2609.26047

Recognizable Picture Languages: Separating UREC from coUREC via Communication Complexity

Antonin Callard·Andrei Romashchenko·Véronique Terrier·Pascal Vanier
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Abstract

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

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Antonin Callard, Andrei Romashchenko, Véronique Terrier, Pascal Vanier. 2026-09-22. Recognizable Picture Languages: Separating UREC from coUREC via Communication Complexity. https://arxiv.org/abs/2609.26047

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